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The Category and Operad of Matching Dialgebras

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Abstract

This paper gives a systematic study of matching dialgebras corresponding to the operad As (2) in Zinbiel (2012) as the only Koszul self dual operad there other than the operads of associative algebras and Poisson algebras. The close relationship of matching dialgebras with semi-homomorphisms and matched pairs of associative algebras are established. By anti-symmetrizing, matching dialgerbas are also shown to give compatible Lie algebras, pre-Lie algebras and PostLie algebras. By the rewriting method, the operad of matching dialgebras is shown to be Koszul and the free objects are constructed in terms of tensor algebras. The operadic complex computing the homology of the matching dialgebras is made explicit.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310027, China

    Yong Zhang

  2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China

    Chengming Bai

  3. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, China

    Li Guo

  4. Department of Mathematics and Computer Science, Rutgers University, Newark, NJ, 07102, USA

    Li Guo

Authors
  1. Yong Zhang
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  2. Chengming Bai
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  3. Li Guo
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Correspondence to Li Guo.

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Zhang, Y., Bai, C. & Guo, L. The Category and Operad of Matching Dialgebras. Appl Categor Struct 21, 851–865 (2013). https://doi.org/10.1007/s10485-012-9290-7

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  • DOI: https://doi.org/10.1007/s10485-012-9290-7

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Mathematics Subject Classifications (2010)

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